scholarly journals Uniqueness of a Planar Contact Discontinuity for 3D Compressible Euler System in a Class of Zero Dissipation Limits from Navier–Stokes–Fourier System

2021 ◽  
Author(s):  
Moon-Jin Kang ◽  
Alexis F. Vasseur ◽  
Yi Wang
Keyword(s):  
Contact Discontinuity ◽  
Euler System ◽  
Navier Stokes ◽  
Compressible Euler ◽  
Planar Contact

scholarly journals Uniform regularity for the free surface compressible Navier–Stokes equations with or without surface tension

2017 ◽  
Vol 28 (02) ◽  
pp. 259-336
Author(s):  
Yu Mei ◽  
Yong Wang ◽  
Zhouping Xin
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Stokes System ◽  
Euler System ◽  
Navier Stokes ◽  
Time Interval ◽  
Uniform Estimates ◽  
Compressible Euler

In this paper, we investigate the uniform regularity of solutions to the three-dimensional isentropic compressible Navier–Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the compressible Euler system for vanishing viscosity and surface tension. It is shown that there exists a unique strong solution to the free boundary problem for the compressible Navier–Stokes system in a finite time interval which is independent of the viscosity and the surface tension. The solution is uniformly bounded both in [Formula: see text] and a conormal Sobolev space. It is also shown that the boundary layer for the density is weaker than the one for the velocity field. Based on such uniform estimates, the asymptotic limits, to the free boundary problem for the ideal compressible Euler system with or without surface tension as both the viscosity and the surface tension tend to zero, are established by a strong convergence argument.

scholarly journals Blowup of Solutions to the Compressible Euler-Poisson and Ideal MHD Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wenming Hu
Keyword(s):  
Finite Time ◽  
Euler System ◽  
Time Dependent ◽  
Poisson System ◽  
Blowup Of Solutions ◽  
Finite Time Blowup ◽  
Ideal Mhd ◽  
Compressible Euler ◽  
Time Blowup

In the present paper, we study the blowup of the solutions to the full compressible Euler system and pressureless Euler-Poisson system with time-dependent damping. By some delicate analysis, some Riccati-type equations are achieved, and then, the finite time blowup results can be derived.

scholarly journals Linear Stability Analysis of Runge–Kutta-Based Partial Time-Splitting Schemes for the Euler Equations

2010 ◽  
Vol 138 (12) ◽  
pp. 4475-4496 ◽  
Author(s):  
Michael Baldauf
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Simulation Models ◽  
Euler System ◽  
Splitting Schemes ◽  
Stability Properties ◽  
Compressible Euler ◽  
Numerical Stability Analysis ◽  
Time Splitting ◽  
Runge Kutta

Abstract For atmospheric simulation models with resolutions from about 10 km to the subkilometer cloud-resolving scale, the complete nonhydrostatic compressible Euler equations are often used. An important integration technique for them is the time-splitting (or split explicit) method. This article presents a comprehensive numerical stability analysis of Runge–Kutta (RK)-based partial time-splitting schemes. To this purpose a linearized two-dimensional (2D) compressible Euler system containing advection (as the slow process), sound, and gravity wave terms (as fast processes) is considered. These processes are the most important ones in limiting stability. First, the detailed stability properties are discussed with regard to several off-centering weights for each fast process described by horizontally explicit, vertically implicit schemes. Then the stability properties of the temporally and spatially discretized three-stage RK scheme for the complete 2D Euler equations and their stabilization (e.g., by divergence damping) are discussed. The main goal is to find optimal values for all of the occurring numerical parameters to guarantee stability in operational model applications. Furthermore, formal orders of temporal truncation errors for the time-splitting schemes are calculated. With the same methodology, two alternatives to the three-stage RK method, a so-called RK3-TVD method, and a new four-stage, second-order RK method are inspected.

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